An atomic force microscope (AFM) is a comparatively high-resolution type of scanning probe microscope. With demonstrated resolution of fractions of a nanometer, AFMs promise resolution more than 1000 times greater than the optical diffraction limit.
Generally, conventional AFMs include a microscale cantilever with a sharp tip (probe) at its end that is used to scan the specimen surface. The cantilever is typically silicon or silicon nitride with a tip radius of curvature on the order of nanometers. When the tip is brought into contact with a sample surface, forces between the tip and the sample lead to a deflection of the cantilever. One or more of a variety of forces are measured via the deflection of the cantilevered probe tip. These include mechanical forces and electrostatic and magnetostatic forces, to name only a few. Typically, the deflection of the cantilevered probe tip is measured using a laser spot reflected from the top of the cantilever and onto an optical detector. Other methods that are used include optical interferometry and piezoresistive AFM cantilever sensing.
A relatively recent type of AFM is a frequency-modulation (FM) AFM (FM-AFM). In addition to inherent speed and extremely high spatial resolution, the FM-AFM may be able to isolate and quantitatively measure both conservative and dissipative tip-sample interactions. However, such measurements are generally tainted by instrumental artifacts, making them irreproducible and controversial. The dissipation signal is corrupted to the extent that researchers call it “apparent dissipation” to encompass its huge variation, unphysical negative values, and contrast inversion.
Recently, these instrumental artifacts have been traced to time delays and “spurious” dynamics of a cantilever excitation system used for oscillating the cantilever. More particularly, the cantilever excitation system of the FM-AFM attempts to oscillate the cantilever on resonance (i.e., at the resonant frequency of the cantilever) by varying the frequency of the sine drive signal to nominally keep cantilever phase at about −90 degrees. For example, at the start of an experiment, the resonant frequency of the cantilever is chosen according to various known techniques, and any spurious difference from −90 degrees is compensated for using an offset in phase. However, the offset becomes inaccurate when the cantilever interacts with the surface of a sample, and the resonant frequency of the cantilever shifts.
Therefore, in order to keep the measured phase constant, a conventional FM-AFM settles on a frequency of the drive signal that is off-resonance by an amount equaling the frequency-dependent change in the spurious phase. Driving the cantilever off-resonance, in turn, causes the amplitude of the cantilever oscillation to decrease. This is compounded by the frequency dependence of the cantilever excitation system, leading to large false variations in the apparent dissipation. These problems are particularly severe for acoustic excitation (described as a “forest of peaks”), but are also significant for direct cantilever excitation methods, such as photothermal and magnetic excitation. In addition, these dynamics cause the maximum frequency response of the cantilever to occur separately from the actual resonant frequency, which may confuse the user. In practice, the cantilever is never actually driven on-resonance, thus violating the fundamental assumptions of quantitative FM-AFM.
In attempts to correct these errors, elaborate measures have been developed to strip away artifacts from measured FM-AFM data using post-processing, which is computationally intense. In addition, the FM-AFM still operates off-resonance, and correct physical signals are not available in real time, either to the user for analysis or to the remainder of the FM-AFM for feedback. Accordingly, there is a need for a system and method that eliminate the artifacts in real time, such that the frequency shift and dissipation signals reflect only actual cantilever physics.